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12 Concerning whether the output curve passes through the origin (or begins to rise

only to the right of the origin), see Knight, F. H., Risk, Uncertainty and Profit, Univer-

sity of London (Reprint), London, 1957, p. 101â€”ftnt.

1 74 MARKET THEORY AND THE PRICE SYSTEM

have lower and lower slopes. This corresponds to rising average product of

Ax until the point M and steadily declining average product thereafter.

It will be readily seen that M, E, correspond to the two points in the

isoquant map where the line GH was intersected by the two ridge lines.

The first stage, described in the laws of variable proportions, thus corre-

sponds to the portion of the curve from G to MÂ°. In this region the average

output of Ay is increasing, and its marginal output is positive and greater

than the average output (as seen by comparing the slope of the output

curve at any point in this region, with the slope of the line joining this

point to the origin). In the diagram, since this portion of the output curve

was drawn concave from above, the marginal output also was increasing

during a portion of the range. The second stage described in the laws of

variable proportions corresponds to the portion of the output curve between

MÂ° and EÂ°. In this region the average and the marginal outputs are both

decreasing (but positive). The third stage corresponds to the region to the

right of EÂ°; average output continues to fall and marginal output is nega-

tive. The points MÂ°, and EÂ°, have the special significance that for point

MÂ° average output of Ay is at a maximum, while at point EÂ° total output

is at a maximum (with marginal output of Ax zero).

Taking the more general approach, with the focus upon the ratio

between the inputs of the two factors rather than on the absolute input of

Alt we can easily see the application of the symmetry noticed earlier. The

situation in the first stage with respect to average and marginal output

of AJt with the quantity of Ax increasing, is completely mirrored in the third

section, with respect to average and marginal outputs of A2 considered for

a steadily decreasing input of Ax. In particular it is true that with constant

returns to scale, wherever the ratio of the input of either of the factors to

that of the other is so low that the average output of the first factor rises

with its increased input, then the situation is such that the other factor is

being so used that its marginal product is negative; output could be in-

creased by discarding some of this other factor. Moreover, at MÂ°, where the

average product of A1 is at a maximum, the marginal output of A2 is zero

(that is, the total output yielded with any fixed quantity of Ax is maximized

when A2 is employed in the proportion denoted by the point M in Figure

8-11); and the converse of this proposition is true at the point EÂ°.

ECONOMIC IMPLICATIONS OF THE

LAWS OF VARIABLE PROPORTIONS

The laws of variable proportions describe the pattern of technical condi-

tions that make up the background of the alternatives the producer-en-

trepreneur is able to choose from. In the market place, the precise

PRODUCTION THEORY 175

determination of these alternatives depends on the prices that quantities of

the factors can be bought at in the market.

Several generalizations can be made immediately. No entrepreneur

will under any circumstances employ a unit of a factor whose employment

causes output to decline. Thus, the laws of variable proportions tell us

immediately that there are opportunities open to the entrepreneur that

he will unquestionably reject. The entrepreneur will not employ factors

in a proportion that fits into either stage one or stage three of possible input

proportions. In either of these regions greater output could be obtained

simply by discontinuing the use of some of the factors. Thus, the very

important result is established that the only portion of the production sur`

face ever seriously under consideration is between the ridge lines. This

means that any group of factors employed in production will be in such a

proportion that (a) the per-unit output of each factor would be lower with

increased input, and (b) the marginal increment of product of any factor

would be lower with increased input. 13 (Increasing average or marginal

products can occur only where one of the factors has negative marginal

product; that is, in the regions outside the ridge lines.)

The goal of the entrepreneur is to produce his output at the lowest

possible cost. Of all the available alternative ways of producing a given

output, there will be one, or several, that require a smaller total outlay

than the others. Or, to put the matter the other way around, of all the

possible levels of output that it is possible to attain with a given cost out-

lay, one or several will be higher than the others. The entrepreneur will

seek to combine inputs in that proportion that will squeeze the most output

out of the cost outlay.

If either of the factors is a free good, it is very simple to determine

the optimum factor proportion. Additional units of this factor can be

obtained, for any given cost outlay, without forgoing the employment of

any of the other factor that it might be desirable to employ. The en-

trepreneur, thus, must simply buy as much of the priced factor as the given

cost outlay permits and then combine with it as much of the free factor as

will maximize output. That is, he must choose the proportion of the factors

at which the marginal output of the free good is zero (which is then also

the point where the average output attributable to the priced factor is at

a maximum). This point, of course, is at the boundary of the middle stage

(within which all entrepreneurs will, as we have seen, necessarily operate)

where the free good is employed relatively more freely.

13 One conceivable exception to these generalizations may result from a producer's

knowledge that the market price of his inputs and outputs depends very sensitively upon

his own production decisions. For the remainder of this chapter wTe ignore this possi-

bility.

1 76 MARKET THEORY AND THE PRICE SYSTEM

THE LEAST-COST COMBINATION

Where, as is the usual case, both factors can be had only at a price, the

problem of determining the least-cost combination of factors for a given

output is very similar to the problem that the consumer faces in allocating

his income among several goods. In both cases the goal will be to ensure

that expenditure is distributed in such a way that were any sum of money

to be withdrawn at the margin from one good in favor of another, the

economizing individual would rank the sacrificed commodities higher on

his value scale than the additional commodities. In the case of the con-

sumer, the comparison involved the marginal utilities of the relevant com-

modities. For the producer the comparison can be made more objectively

in terms of the output given up, and the additional output gained. Thus

the least-cost factor combination, which the entrepreneur will consciously

seek to achieve, will be attained when the marginal increment of product

corresponding to the last "dollar's" worth of expenditure upon any one

factor is greater than the marginal increment of product corresponding to

a prospective additional expenditure of a dollar upon any other factor. If

this situation does not prevail, there is room to gain output, on balance, by

withdrawing money spent at the margin on one factor and expanding by

this amount the sum spent on other factors. This transfer will go on with

the consequence that the marginal increment of output corresponding to

the factor from which expenditure is being withdrawn will steadily rise

(because according to the law of variable proportions the relevant stage is

always that where the marginal output falls with greater inputs), while that

of the factors whose use is being expanded will fall, until the least-cost

combination is attained.

It is easy to see that with small-sized marginal units of factor (with

which the difference between the marginal increments of output corre-

sponding to two successively acquired units of factor can be ignored), this

least-cost combination condition can be stated as follows. The marginal

increments of product corresponding to units of any two factors must be

in the same proportion to one another as are their prices (MIPAl/MIPÃ„2 =

price of ^j/price of A2). A given sum of money (S) being spent at the

margin on A2 (buying the quantity S/PAo, with PÃ„9 the price of A2) makes a

difference to output responsible for S x MIPAo/PA(Ã¬ output (approximately);

whereas the same amount of money spent on additional units of A1 could buy

V^Â¿i units > which could add (approximately) S X MIPAi/PAi in additional

output. But if, say, MIPAJM1PA2 > PAl/PÃ„2 then MlPAJPAl > MIPÃ„2/PÃ„2

so that the transfer of expenditure at the margin from A2 to Ax would be

worthwhile. Thus, only equality between the two fractions describes the

situation where the least-cost combination has been attained.

177

PRODUCTION THEORY

GRAPHIC ILLUSTRATION OF THE LEAST-COST COMBINATION

The isoquant map provides, once again, a useful means for visualizing

the particular choice of input proportions that an entrepreneur will make

under given cost conditions. It is necessary to introduce once more a

graphic device that we have already met in the theory of consumer income

allocationâ€”the constant expenditure curve. It will be recalled that if any

two goods, Ax and A2, can be obtained in any amount at constant prices per

unit (PAl and PÂ¿2 respectively), then a line (BC in Figure 8-12) can be drawn

Figure 8-12

tracing out all the different packages of the two goods that a given sum of

money (say, S) can buy. For such a line, OB = S/PÃ„2, and OC = S/PAl, so

that the slope BC with respect to the A1 axis is equal to PÂ±JPA^` I*1 t n e

case of production, such a line passes through all the different factor com-

binations that can be bought for a given cost outlay and is given the name

isocost line.

When the isocost line is superimposed on an isoquant map, the points

where the isocost line is intersected by successive isoquants rank the differ-

ent factor combinations in order of their productive efficiency. The

particular choice of input proportions the entrepreneur seeks to achieve

corresponds to the point on an isocost line where it meets the highest of

these attainable isoquant levels.

In Figure 8-13 the isocost line BC (corresponding to a ratio of PAJPAÂ» â€”

OB/OC) is superimposed upon an isoquant map. It is evident that the

point P on the isocost corresponds to the particular factor combination that

yields highest output. It is at this point that the isocost is just tangent to an

isoquant. An any other point (for example, at T) the isocost can only

cut an isoquant; thus, there is a higher level of output that can be obtained

by giving up some of one input (for example, A2) and employing instead

additional units of the other (AA). At P, a transfer in either direction

178 MARKET THEORY AND THE PRICE SYSTEM

would be disadvantageous because it could result only in lower output.

Any level of output higher than at P is simply out of reach with this outlay.

It will be observed that at the point of tangency, the slope of the

isoquant line is the same as that of the isocost; thus, this point fulfills the

(approximate) condition that the additional quantity of any one factor

necessary to offset the withdrawal from production of one unit of the

Figure 8-13

other factor be equal to the ratio of the price per unit of the second factor

to the price per unit of the first. This, of course, is simply the same

condition developed in the previous section, that the ratio between the

marginal increments of product corresponding to units of the two factors

be equal to the ratio of their prices.14

This graphic derivation of the least-cost condition provides an inter-

esting illustration of several of the principles developed in earlier sections

of this chapter. Thus the significance of the fact that the factors are not

perfect substitutes for one another is clearly brought out. If factors were

perfect substitutes so that the isoquants were straight lines, then, if the

slope of these isoquants were different from that of the isocost, there would

be no point of tangency at all. Substitution of one factor for another

would continue until only the one factor would be used. If the slope of

14 It may be observed at this point that much of the isoquant geometry developed in

this chapter has, in the literature, a counterpart in consumer theory. In the literature

the formal and diagrammatic analogy between consumer theory and production theory

has been carried forward very extensively. Corresponding to the isoquant map in produc-

tion theory, economists discuss the indiÃŸerence curve map in the theory of the consumer.

An indifference curve is a line drawn through all those different possible combinations

of two commodities between which a consumer feels indifferent. The approach to

consumer theory adopted in Chs. 4 and 5 made it unnecessary to resort to the use of

indifference curves (concerning which there are some rather serious theoretical problems).

The detailed discussion of isoquant maps in the present chapter, however, may be

applied to consumer theory without significant alteration if it is desired to employ the

indifference curve technique.

179

PRODUCTION THEORY

the isocost was that of the isoquants, then the isocost would coincide with

an isoquant throughout its length; thus, no particular proportion between

the two factors can be pronounced the most economic. (This, in fact,

would be the case where, as we saw, the two factors make up one homo-

geneous group. The equality in isocost and isoquant slopes simply means

that different prices are not being charged for economically identical units

of factors.)

FC

Figure 8-14

Movement along an isoquant corresponds to an alteration of input

proportions. The fact that one such proportion is better than the others

is the corollary of the fact that the factors are not perfect substitutes for

each other. A change in the slope of the isocost (corresponding to a

relative cheapening of one of the factors, compared with the other) will

alter the point of tangency, either making a higher output possible for

the same outlay or bringing down the possible level of output. In any

event such a change will alter the optimum proportions of input in favor

of the factor that has become relatively cheaper.15

With a given relation between factor prices, it is possible to draw a

series of isocost lines, as BC, DE, FG . . . (in Figure 8-15). The respective

15 By an extension of the analysis of the least-cost combination, an insight can be

obtained into the notion of the demand curve for a factor of production. Such a curve,

for any one producer, reflects the different quantities of the factor that he asks to buy

at respectively different prices (all other things remaining unchanged). The lower the

price of a factor, the larger will be the quantity that a producer will generally wish to

buy. Our analysis explains part of the reason for this: the lower the price of a factor,

the more it pays to substitute it in place of other factors. The lower the price of a

factor, the greater becomes the marginal product derived from the last dollar spent on

it. Consequently the producer must (even if he were not to expand his output as the

result of the lower costs) switch expenditure at the margin from other resources to the

now cheaper resource, in order to achieve the (new) least-cost combination. (See also

Ch. 9, p. 200, ftnt. 10.)

MARKET THEORY AND THE PRICE SYSTEM

180

points of tangency on these lines correspond to the different factor com-

binations that are optimum for successively higher levels of cost outlay.

Each such point makes the most of the relevant cost outlay; the entrepre-

neur has to select that level of outlay, which, taken in conjunction with

the price he can expect to get for his output, maximizes profits. The

path joining these points of tangency is appropriately named the expansion

path.

0 CÂ£ G I A%

Figure 8-15

We can refer graphically, finally, to the special case where one of the

factors is a free good, costing nothing to obtain. In this case, the isocost

line will be a straight line parallel to the axis of the free input. It will

show that a fixed quantity of the non-free input can be employed, with no

limit on the free input. The point of tangency with the isoquants will

be where the isoquants are vertical or horizontal; that is, on the ridge line.

(o)

PRODUCTION THEORY 1 81

At this point, as much of the free input is being used as can be employed

without diminishing possible output.

SUMMARY

Chapter 8 commences the analysis of the activity of the individual

market participant in the role of producer. This analysis serves as the

foundation for the examination of the supply side of the market. The

economist sees the producer as making choices among alternatives of a

special kind. These alternatives involve the various productive uses that

the resources available to him might be put to. The rejected productive

uses constitute the economic costs of production of any adopted process

of production involving scarce resources. In society the efficiency of pro-

duction is advanced through specialization and division of labor. The

producer's alternatives are rigidly controlled by the market prices of the

resources he must purchase for a given production process.

Production is carried on with factors of production. A unit of factor

may possibly be related to a second unit of factor in a substitute relation-

ship, or possibly in a complementary relationship. A unit of factor may be

specific to the production of a certain product; it may be specialized for

this particular production; or, on the other hand, it may be versatile in

production.

Analysis of production decisions is formalized by the use of several

mathematical and graphical concepts. Production possibilities are ex-

pressed in the production function, expressed graphically as the produc-

tion surface. Contour lines on this surface are isoquants. The slope of

the isoquants measure the substitutability between the cooperating factors.

Extreme cases are those where either no substitution at all is possible

(technically rigid proportions being required), or where the one factor may

be substituted completely for the second. Typical production processes

permit substitution between the complementary factors to a limited degree.

The isoquant geometry points up clearly the distinction between al-

terations in the proportions in which factors are combined, and alterations

in the scale in which factors (combined in a given proportion) are applied.

Alterations in scale yield alterations in output that may be characterized

by increasing returns to scale, decreasing returns to scale, or constant re-

turns to scale. Alterations in factor proportions yield alterations in out-

put that are governed by the laws of variable proportions. Detailed anal-

ysis of the various possible cases throws light on the alternative possible

ways of expressing these laws.

The economic implications of the laws of variable proportions include

the delimitation of the best input combination a producer will employ

1 82 MARKET THEORY AND THE PRICE SYSTEM

under given technical and market conditions. The attainment of this

"least-cost combination" may be analyzed both logically and graphically.

Suggested Readings

Knight, F. H., Risk, Uncertainty and Profit, University of London (Reprint), Lon-

don, 1957, Ch. 4.

Carlson, S., A Study on the Pure Theory of Production, Kelley and Millman Inc.,

New York, 1956.

Stonier, A. W.â€”Hague, W. C , A Textbook of Economic Theory, Longmans Green,

London, 1953, Ch. 10.

Costs and Supply

A, of the operation

.N UNDERSTANDING

of the full market process must include, we have seen, the understanding

of the forces acting to supply the market with the various produced goods

and services. These forces determine the arrays of alternatives offered to

prospective consumers. But we have seen that these forces are themselves

conditioned by the circumstances under which entrepreneurs are able to

engage in production. In particular the entrepreneur operates in a situ-

ation where his choice of product, his choice of production method, and

his choice of volume of production must be made on the basis of the

market facts relating to the prices of both products and factors. In order

to produce any particular quantity of a particular product in a particular

way, the entrepreneur must pay definite costs of production. The quantity

of any one product that an entrepreneur will contribute to the market

supply, thus, will depend partly on the costs incurred for this output. The

quantity that the market as a whole will supply of any one product will

in turn depend partly on the costs of production that must be incurred

individually by entrepreneurs for the various possible levels of output.

In this chapter we carry further the analysis of the forces of supply.

Leaning heavily on the principles of production discussed in the previous

chapter, we examine especially the way costs of production of firms in a

particular industry are likely to change with output. The chapter carries

through the analysis to include the way the entrepreneur reacts to these

alternative production opportunities and the way is thus cleared to the

understanding of the forces of supply as they finally impinge on the market.

The focus of attention in this chapter is thus rather different from

that of the previous chapter. There we studied production, examining

the way output depended on the particular input combination employed.

Here we adopt a point of view corollary to that of the previous chapter;

183

1 84 MARKET THEORY AND THE PRICE SYSTEM

here we are principally concerned with the way the costs of the firm depend

on the level of output. Unless otherwise specified, it may be assumed

throughout the chapter that for each output level, the least-cost combina-

tion problem has been solved. We turn first to a review of the ultimate

meaning of cost and its place in production theory.

COSTS AND RENTS

The cost concept is bound up inseparably with the concept of human

action. Action consists in choosing between alternatives. The adoption

of any one specific alternative implicitly involves the rejection of other

alternatives; in particular it involves the rejection of the "second-best"

alternativeâ€”namely, that alternative that would have been adopted had

the alternative that was actually adopted been unavailable. It is this

rejected alternative that the economizing individual recognizes as the cost

of the adopted alternative simply because both opportunities cannot be

simultaneously adopted. A man may have to choose between the chance

of opening a certain kind of store on the one hand, and retaining the

friendship of a man engaged in the same line of business, on the other

hand. If he adopts the former alternative, then he recognizes that his

business has cost him his neighbor's friendship. Should he value the

friendship more highly, then the cultivation and preservation of this friend-

ship has cost him a possible lucrative business opening. Cost is made up

of the conscious sacrifice of an available opportunity. This is the most

general conception of the cost category.

For the isolated individual, the act of production involves a particular

aspect of cost. The employment of a unit of a non-specific resource for

the production of one particular product necessarily withholds it from

making any contribution to the production of other products. A decision

to make any particular use of a resource thus involves the sacrifice of other

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